## Description

1) [4 points] Prove that 9 | (4#$ + 8) for every integer � ≥ 0.

2) [4 points] Prove that ∑ (8� − 5) $

/01 = 4�3 − � for every positive integer n.

3) [4 points] Prove that 13 + 23 + 33 + 43 + ⋯ + �3 = $($91)(3$91)

: for every positive

integer n.